Mechanisms for tuning clustering and degree-correlations in directed networks

With complex networks emerging as an effective tool to tackle multidisciplinary problems, models of network generation have gained an importance of their own. These models allow us to extensively analyze the data obtained from real-world networks, study their relevance and corroborate theoretical results. In this work, we introduce methods, based on degree preserving rewiring, that can be used to tune the clustering and degree-correlations in directed networks with random and scale-free topologies. They provide null-models to investigate the role of the mentioned properties along with their strengths and limitations. We find that in the case of clustering, structural relationships, that are independent of topology and rewiring schemes are revealed, while in the case of degree-correlations, the network topology is found to play an important role in the working of the mechanisms. We also study the effects of link-density on the efficiency of these rewiring mechanisms and find that in the case of clustering, the topology of the network plays an important role in determining how link-density affects the rewiring process, while in the case of degree-correlations, the link-density and topology, play no role for sufficiently large number of rewiring steps. Besides the intended purpose of tuning network properties, the proposed mechanisms can also be used as a tool to reveal structural relationships and topological constraints.Comment: 8 pages, 11 figures, submitted to Physical Review

Cognitive modelling of language acquisition with complex networks

ABSTRACT Cognitive modelling is a well-established computational intelligence tool, which is very useful for studying cognitive phenomena, such as young children's first language acquisition. Specifically, linguistic modelling has recently benefited greatly from complex network theory by modelling large sets of empirical linguistic data as complex networks, thereby illuminating interesting new patterns and trends. In this chapter, we show how simple network analysis techniques can be applied to the study of language acquisition, and we argue that they reveal otherwise hidden information. We also note that a key network parameter -the ranked frequency distribution of the links -provides useful knowledge about the data, even though it had been previously neglected in this domain

Temporal ordering of input modulates connectivity formation in a developmental neuronal network model of the cortex

Preterm infant brain activity is discontinuous; bursts of activity recorded using EEG (electroencephalography), thought to be driven by subcortical regions, display scale free properties and exhibit a complex temporal ordering known as long-range temporal correlations (LRTCs). During brain development, activity-dependent mechanisms are essential for synaptic connectivity formation, and abolishing burst activity in animal models leads to weak disorganised synaptic connectivity. Moreover, synaptic pruning shares similar mechanisms to spike-timing dependent plasticity (STDP), suggesting that the timing of activity may play a critical role in connectivity formation. We investigated, in a computational model of leaky integrate-and-fire neurones, whether the temporal ordering of burst activity within an external driving input could modulate connectivity formation in the network. Connectivity evolved across the course of simulations using an approach analogous to STDP, from networks with initial random connectivity. Small-world connectivity and hub neurones emerged in the network structure—characteristic properties of mature brain networks. Notably, driving the network with an external input which exhibited LRTCs in the temporal ordering of burst activity facilitated the emergence of these network properties, increasing the speed with which they emerged compared with when the network was driven by the same input with the bursts randomly ordered in time. Moreover, the emergence of small-world properties was dependent on the strength of the LRTCs. These results suggest that the temporal ordering of burst activity could play an important role in synaptic connectivity formation and the emergence of small-world topology in the developing brain

Modeling the clustering in citation networks

For the study of citation networks, a challenging problem is modeling the high clustering. Existing studies indicate that the promising way to model the high clustering is a copying strategy, i.e., a paper copies the references of its neighbour as its own references. However, the line of models highly underestimates the number of abundant triangles observed in real citation networks and thus cannot well model the high clustering. In this paper, we point out that the failure of existing models lies in that they do not capture the connecting patterns among existing papers. By leveraging the knowledge indicated by such connecting patterns, we further propose a new model for the high clustering in citation networks. Experiments on two real world citation networks, respectively from a special research area and a multidisciplinary research area, demonstrate that our model can reproduce not only the power-law degree distribution as traditional models but also the number of triangles, the high clustering coefficient and the size distribution of co-citation clusters as observed in these real networks

Network of recurrent events for the Olami-Feder-Christensen model

We numerically study the dynamics of a discrete spring-block model introduced by Olami, Feder and Christensen (OFC) to mimic earthquakes and investigate to which extent this simple model is able to reproduce the observed spatiotemporal clustering of seismicty. Following a recently proposed method to characterize such clustering by networks of recurrent events [Geophys. Res. Lett. {\bf 33}, L1304, 2006], we find that for synthetic catalogs generated by the OFC model these networks have many non-trivial statistical properties. This includes characteristic degree distributions -- very similar to what has been observed for real seismicity. There are, however, also significant differences between the OFC model and earthquake catalogs indicating that this simple model is insufficient to account for certain aspects of the spatiotemporal clustering of seismicity.Comment: 11 pages, 16 figure

Structural transitions in scale-free networks

Real growing networks like the WWW or personal connection based networks are characterized by a high degree of clustering, in addition to the small-world property and the absence of a characteristic scale. Appropriate modifications of the (Barabasi-Albert) preferential attachment network growth capture all these aspects. We present a scaling theory to describe the behavior of the generalized models and the mean field rate equation for the problem. This is solved for a specific case with the result C(k) ~ 1/k for the clustering of a node of degree k. Numerical results agree with such a mean-field exponent which also reproduces the clustering of many real networks.Comment: 4 pages, 3 figures, RevTex forma